K-theory
noun ·Rare ·Advanced level
Definitions
- 1 The study of rings R generated by the set of vector bundles over some topological space or scheme; uncountable
"K'''-theory as an independent discipline is a fairly new subject, only about 35 years old."
- 2 The study of rings R generated by the set of vector bundles over some topological space or scheme; (dated, obsolete) that part of algebraic topology comprising what is now called topological K-theory.; that part of algebraic topology comprising what is now called topological K-theory. dated, obsolete, uncountable
- 3 The cohomology generated by the set of vector bundles over some topological space or scheme. countable
"The theory of formal groups has found a number of rather spectacular applications in recent years in number theory, arithmetical algebraic geometry, algebraic geometry, and algebraic topology, ranging from congruences for the coefficients of modular forms and local class field theory to extraordinary K'''-theories and (indirectly) results on the homotopy groups of spheres."
Example
More examples"K'''-theory as an independent discipline is a fairly new subject, only about 35 years old."
Etymology
From circa 1960. The K stands for German Klasse (“class”). The theory developed out of algebraic geometry after the 1957 publication of work by German-born French mathematician Alexander Grothendieck.
Related phrases
More for "k-theory"
Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.